# Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree Basic Math Facts – Exponents

You are searching about Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree, today we will share with you article about Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree was compiled and edited by our team from many sources on the internet. Hope this article on the topic Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree is useful to you.

Page Contents

## Basic Math Facts – Exponents

Exponents make up a juicy tidbit of basic math material. Exponents allow us to raise numbers, variables and even expressions to powers, thus achieving repeated multiplication. The exponent always present in all kinds of mathematical problems requires the student to be well acquainted with its characteristics and properties. Here we look at the laws, the knowledge of which will allow any student to master this topic.

In the expression 3^2, which reads “3 squared”, or “3 to the second power”, 3 is the base and 2 is the power or exponent. The exponent tells us how many times to use the base as a factor. The same applies to variables and variable expressions. In x^3, this means x*x*x. In (x + 1)^2, this means (x + 1)*(x + 1). Exponents are ubiquitous in algebra and throughout mathematics, and understanding their properties and how to work with them is extremely important. Mastery of exponents requires the student to be familiar with some basic laws and properties.

The law of the product

When multiplying expressions involving the same base to different or equal powers, simply write the base to the sum of the powers. For example, (x^3)(x^2) is the same as x^(3 + 2) = x^5. To see why this is so, think of the exponential expression as beads on a string. In x^3 = x*x*x, you have three x’s (beads) on the string. In x^2, you have two beads. So in the product you have five pearls, ox^5.

Quotient law

When you divide expressions that involve the same base, simply remain the powers. Thus in (x^4)/(x^2) = x^(4-2) = x^2. Because this is so dependent on the cancellation property of real numbers. This property says that when the same number or variable appears in the numerator and the denominator of a fraction, then this term can be canceled. Let’s look at a numerical example to make this completely clear. Take (5*4)/4. Since 4 appears at the top and bottom of this expression, we can kill — well not kill, we don’t want to be violent, but you know what I mean — to get 5. Now let’s multiply and divide to see if he agrees with our answer: (5 * 4) / 4 = 20/4 = 5. Check. So this cancellation property holds. In an expression like (y^5)/(y^3), this is (y*y*y*y*y)/(y*y*y), if expanded. Since we have 3 y in the denominator, we can use those to cancel 3 y in the numerator to get y^2. This agrees with y^(5-3) = y^2.

The power of a power law

In an expression like (x^4)^3, we have what is known as a power to a power. The power of a power law says that we simplify by multiplying the powers together. Thus (x^4)^3 = x^(4*3) = x^12. If you are wondering why this is so, note that the base in this expression is x^4. The exponent 3 tells us to use this base 3 times. Thus we get (x^4)*(x^4)*(x^4). Now we see this as a product of the same base to the same power and can thus use our first property to obtain x^(4 + 4+ 4) = x^12.

Distributive property

This property tells us how to simplify an expression like (x^3*y^2)^3. To simplify this, we distribute the power 3 outside the parentheses inside, multiply each power to get x^(3*3)*y^(2*3) = x^9*y^6. To understand why this is so, note that the base in the original expression is x^3*y^2. The 3 outer parentheses tell us to multiply this base by itself 3 times. When you do that and then rearrange the expression using the associative and commutative properties of multiplication, you can apply the first property to get the answer.

Property of Zero Exponent

Every number or variable — except 0 — to the power 0 is always 1. Thus 2 ^ 0 = 1; x^0 = 1; (x + 1)^0 = 1. To see why this is so, consider the expression (x^3)/(x^3). This is clearly equal to 1, since any number (except 0) or expression on its own yields this result. Using our quotient property, we see that this is equal to x^(3 – 3) = x^0. Since both expressions must give the same result, we have that x^0 = 1.

Property of negative exponent

When we raise a number or variable to a negative integer, it ends with u reciprocal. It is 3^(-2) = 1/(3^2). To see why this is so, consider the expression (3^2)/(3^4). If we expand this, we get (3 * 3) / (3 * 3 * 3 * 3). Using the cancellation property, you end up with 1/(3*3) = 1/(3^2). Using the quotient property, we have that (3^2)/(3^4) = 3^(2 – 4) = 3^(-2). Since these two expressions must be equal, we have that 3^(-2) = 1/(3^2).

Understanding these six properties of exponents will give students the solid foundation they need to tackle all kinds of pre-algebra, algebra, and even calculus problems. Often, a student’s stumbling blocks can be removed with the bulldozer of foundational concepts. Study these properties and learn. Then you will be on the road to mathematical mastery.

## Question about Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree

If you have any questions about Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree, please let us know, all your questions or suggestions will help us improve in the following articles!

The article Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree was compiled by me and my team from many sources. If you find the article Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree helpful to you, please support the team Like or Share!

Rate: 4-5 stars
Ratings: 7400
Views: 80132370

## Search keywords Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree

Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree
way Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree
tutorial Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree
Foreign Language Instruction Should Begin In The Kindergarten.Do You Agree free
#Basic #Math #Facts #Exponents

Source: https://ezinearticles.com/?Basic-Math-Facts—Exponents&id=6619964

## Example Of A Programming Language Used To Develop Web-Based Application Android VS iOS Application Testing

You are searching about Example Of A Programming Language Used To Develop Web-Based Application, today we will share with you article about Example Of A Programming Language…

## English Became A World-Wide Language For Several Reasons. England Started Make Your Business Global – Understand How Multilingual Website Marketing Can Work to Your Advantage

You are searching about English Became A World-Wide Language For Several Reasons. England Started, today we will share with you article about English Became A World-Wide Language…

## Do You Have To Be Accepted Into A Speech-Language Pathology From Stuttering to Fluent Speech Through Memorization

You are searching about Do You Have To Be Accepted Into A Speech-Language Pathology, today we will share with you article about Do You Have To Be…

## Discuss The Three Primary Features Of An Object-Oriented Programming Language API Writing – As Technical As Technical Writing Gets

You are searching about Discuss The Three Primary Features Of An Object-Oriented Programming Language, today we will share with you article about Discuss The Three Primary Features…

## Determine The Place Of English In The Indo-European Language Family Top Holiday Destinations For British Holiday Makers

You are searching about Determine The Place Of English In The Indo-European Language Family, today we will share with you article about Determine The Place Of English…

## Describe 2 Advantages Of High-Level Programing Over Machine-Language Programming The Evolution of Project Management

You are searching about Describe 2 Advantages Of High-Level Programing Over Machine-Language Programming, today we will share with you article about Describe 2 Advantages Of High-Level Programing…